CBSE Class 9 Maths Sample Paper Set 2
SUBJECT: MATHEMATICS
CLASS : IX
MAX. MARKS : 80
DURATION : 3 HRS
General Instruction:
(i) All questions are compulsory.
(ii) This question paper contains 30 questions divided into four Sections A, B, C and D.
(iii) Section A comprises of 6 questions of 1 mark each. Section B comprises of 6 questions
marks each. Section C comprises of 10 questions of 3 marks each and Section D comprises
questions of 4 marks each.
(iv) There is no overall choice. However, an internal choice has been provided in two questions
mark each, two questions in 2 marks each, four questions of 3 marks each and three questions
marks each. You have to attempt only one of the alternatives in all such questions.
(v) Use of Calculators is not permitted
of 2
of 8
in 1
of 4
SECTION – A
Questions 1 to 6 carry 1 mark each.
1. Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)
OR
Find the height of cone, if its slant height is 34 cm and base diameter is 32 cm.
2. If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.
3. Simplify:
32  48
8  12
OR
Find the value of
3 2 .
4. In a bag, there are 100 bulbs out of which 30 are defective ones. A bulb is taken out of the bag
at random. Find the probability of the selected bulb to be a good one.
5. If its perimeter of an equilateral triangle is 180 cm, what will be its area?
6. In the below figure,  ABC = 69°,  ACB = 31°, find  BDC.
SECTION – B
Questions 6 to 12 carry 2 marks each.
7. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will
fall into the sea in a minute?
8. Find the value of x3 + y3 + 15xy – 125 if x + y = 5.
OR
Find the remainder when 4x3 – 3x2 + 4x – 2 is divided by (i) x – 1 (ii) x – 2
9. The following observations have been arranged in ascending order. If the median of the data is
63, find the value of x.
29, 32, 48, 50, x, x + 2, 72, 78, 84, 95
10. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
11. Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.
OR
Calculate the area of trapezium as shown in the figure:
12. In the below figure, ABCD is a parallelogram, AE  DC and CF  AD. If AB = 16 cm, AE =
8 cm and CF = 10 cm, find AD.
SECTION – C
Questions 13 to 22 carry 3 marks each.
13. In the below figure, ABCD is a quadrilateral and BE || AC and also BE meets DC produced at
E. Show that area of Δ ADE is equal to the area of the quadrilateral ABCD.
OR
Show that a median of a triangle divides it into two triangles of equal areas.
14. Factorise x3 – 23x2 + 142x – 120.
15. A die is rolled 300 times and following outcomes are recorded:
1
2
3
4
5
Outcome
42
60
55
53
60
Frequency
Find the probability of getting a number (i) more than 4 (ii) less than 3
6
30
16. A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle
being 9 cm, 28 cm and 35 cm. Find the cost of polishing the tiles at the rate of 50p per cm2.
17. If a point C lies between two points A and B such that AC = BC, then prove that AC =
1
AB.
2
Explain by drawing the figure.
18. Solve the equation 2x + 1 = x – 3, and represent the solution(s) on (i) the number line, (ii) the
Cartesian plane.
19. AB is a line-segment. P and Q are points on opposite sides of AB such that each of them is
equidistant from the points A and B (see below left figure). Show that the line PQ is the
perpendicular bisector of AB.
OR
ABCD is a quadrilateral in which AD = BC and  DAB =  CBA (see the above right sided
figure). Prove that (i) Δ ABD  Δ BAC (ii) BD = AC (iii)  ABD =  BAC.
20. In the below left figure, if AB || CD, CD || EF and y : z = 3 : 7, find x.
OR
In the above right sided figure, if AB || CD, EF  CD and GED = 126°, find  AGE,  GEF
and  FGE.
21. A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a
point on the minor arc and also at a point on the major arc.
5 2 3
 ab 3
74 3
OR
3 2
3 2

by rationalizing the denominator.
3 2
3 2
22. Find the value of a and b in
Simplify
SECTION – D
Questions 23 to 30 carry 4 marks each.
4
23. Find the value of
 216 
2
3

1
 256 
3
4

2
1
 243 5
24. A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the
cost of Rs 498.96. If the cost of white-washing is Rs 2.00 per square metre, find the (i) inside
surface area of the dome, (ii) volume of the air inside the dome.
OR
Monica has a piece of canvas whose area is 551 m2. She uses it to have a conical tent made,
with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred
while cutting, amounts to approximately 1 m2, find the volume of the tent that can be made with
it.
25. Construct a triangle XYZ in which  Y = 30°,  Z = 90° and XY + YZ + ZX = 11 cm.
26. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a
rhombus.
OR
Prove that “The line-segment joining the mid-points of any two sides of a triangle is parallel to
the third side and is half of it.”
27. Plot the points A (4, 4) and (–4, 4) on a graph sheet. Join the lines OA, OB and BA. What figure
do you obtain.
28. A man hired an auto for 5 km. The fare was 10 for first km and 3 for every subsequent km. He
paid 50, to which the auto driver said that its not the correct amount. The actual fare is
somewhat less than that the amount you have paid to me.
(i) Calculate the correct fare.
(ii) Which value is being promoted by the auto driver?
29. The following table gives the life times of 400 neon lamps:
Life time (in hours) Number of Lamps
300 – 400
14
400 – 500
56
500 – 600
60
600 – 700
86
700 – 800
74
800 – 900
62
900 – 1000
48
(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a life time of more than 700 hours?
30. If x3 + ax2 + bx + 6 has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3),
find the values of a and b.
OR
Without actual division, prove that 2x4 – 6x3 +3x2 +3x – 2 is exactly divisible by x2 – 3x + 2.